BaseCase

;Exercise 1.1 - Given the Scheme code, what's the output?

10
;10

(+ 5 3 4)
;12

(- 9 1)
;8

BaseCase

;Exercise 1.2 - 
(/ (+ 5 4
      (- 2
	 (- 3
	    (+ 6
	       (/ 4 5)))))
   (* 3
      (- 6 2)
      (- 2 7)))

BaseCase

;Exercise 1.3 - Define a procedure that takes three numbers 
;  and returns the sum of the squares of the two larger numbers.

(define (sum-of-squares a b)
  (+ (* a a) (* b b)))

(define (foo a b c)
  (cond ((and (>= a c) (>= b c)) (sum-of-squares a b))
         ((and (>= a b) (>= c b)) (sum-of-squares a c))
         ((and (>= b a) (>= c a)) (sum-of-squares b c))))

BaseCase

;Exercise 1.4 - Describe the behavior of the following prodcedure:
(define (a-plus-abs-b a b)
  ((if (> b 0) + -) a b))

BaseCase

;Exercise 1.5 - Applicative vs normal-order evaluation.
;given this code:
(define (p) (p))

(define (test x y)
  (if (= x 0)
      0
      y))

;what happens when we evaluate this?

BaseCase

;first snippet
(define (+ a b)
  (if (= a 0)
      b
      (inc (+ (dec a) b))))

;second snippet
(define (+ a b)
  (if (= a 0)
      b

BaseCase

;Exercise 1.11 - Given a function f, define two versions of 
; a procedure that computes f, one which generates a 
; tree recursive process, and one that generates an 
; iterative process.

;recursive version:
(define (f n)
  (if (< n 3)
      n
      (+ (f (- n 1)) 

BaseCase

;Exercise 1.12 - Write a procedure that computes elements of 
; Pascal's Triangle via a recursive process.
(define (pascal row col)
  (if (or (= row col) (= col 1))
      1
      (+ (pascal (- row 1) (- col 1)) (pascal (- row 1) col))))

BaseCase

;Exercise 1.29- Define a procedure that uses Simpson's Rule to compute the integral
; of a function. Also, compare this proc with another one in the text.

;to do this one, we need the cube procedure from the text:
(define (cube x)
  (* x x x))

;and also the sum procedure:
(define (sum term a next b)
  (if (> a b)

BaseCase

(define (cons x y)
  (define (dispatch m)
    (cond ((= m 0) x)
          ((= m 1) y)
          (else (error "Argument not 0 or 1"))))
  dispatch)